Multiple choice

How many spherical lead shots each $4.2 cm $ in diameter can be obtained from a rectangular solid (cuboid) of lead with dimensions $66 cm, 42 cm, 21 cm$. (Take $\pi\, =\, \dfrac {22}{7}$)

  1. $1500$
  2. $1200$
  3. $1300$
  4. $1600$
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A Correct answer
Explanation

Volume of cuboid = 66 * 42 * 21 = 58212 cm^3. Volume of one spherical shot = (4/3) * pi * r^3 = (4/3) * (22/7) * (2.1)^3 = (4/3) * (22/7) * 9.261 = 38.808 cm^3. Number of shots = 58212 / 38.808 = 1500.

AI explanation

To find the number of lead shots, divide the volume of the cuboid by the volume of a single spherical shot. The volume of the cuboid is the product of its dimensions, giving 66 times 42 times 21, which equals 58212 cubic cm. The radius of each shot is 2.1 cm, so the volume of one sphere is four thirds times twenty-two sevenths times 2.1 cubed, giving 38.808 cubic cm. Dividing the total volume 58212 by the volume of one shot 38.808 gives exactly 1500 shots.

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